(a)
In the diagram
(i) The value of x; (ii)
(b) If (2N4_{seven} = 15N_{nine}), find the value of N.
Explanation
(a)
(i) In the diagram,
(x° + 90° = (3x + 15)°) (Sum of opposite interior angles)
Thus, (90° – 15° = 3x – x implies 75° = 2x)
(x = 37.5°)
(ii)
< RSQ = 90° – 37.5° = 52.5°
(b) (2N4_{seven} = 15N_{nine})
(2N4_{seven} = (2 times 7^{2}) + (N times 7^{1}) + (4 times 7^{0}))
= (98 + 7N + 4)
= (102 + 7N)
(15N_{nine} = (1 times 9^{2}) + (5 times 9^{1}) + (N times 9^{0}))
= (81 + 45 + N)
= (126 + N)
(implies 102 + 7N = 126 + N)
(7N – N = 126 – 102 = 24)
(6N = 24 implies N = 4)
Therefore, (244_{seven} = 154_{nine}).